Bitcoin has a limit to the number of tokens it will release. That number is hard-coded at 21 million. The estimated date of Bitcoin issuing its last coin is believed to be in the year 2140. No one can predict what will happen at that point, but miners will always earn some profit from transaction fees. Plus, users of the blockchain and the Bitcoins themselves will be incentivized to protect the network, because if mining stops, Bitcoins become vulnerable and so does the data that has been locked into the blockchain.
Do you really need to worry about things that will happen after your death ? 2140 is really very far and bitcoins might not be able to survive by then. If you are still interested in the answer, if bitcoins survived till the last coin was mined, it will be because it becomes a commonly used payment option. And in that case, I see the demand only increasing more in future. Since the supply will reduce as no more mining is done, prices will move up faster.